Theres only 3 options. Priciest to least.
1. Send in your console to have a capture card installed. Wait a while for the console to return. This roughly costs about under 220-490 dollars just for the O3DS XL version from what I've seen around the net.
2. Upgrade to a New 3DS/New 2DS and record with BootNTR. ($199.99 for the New 3DS XL, $159.99 for the New 3DS, $149.99 for the New 3DS XL, also $11 for a flashcart to install CFW with ntrboot)
3. Use a small Tripod, a stand for your 3DS, your Smartphone, a computer, aux cable, and the phones usb port. Crop the said gameplay video on your computer and then upload it wherever you want. Assuming that you have all of these except the tripod, this should cost you at the minimum $5.
Sorry but you are gonna end up having to buy a good amount of materials if you want to do this kind of thing. Hopefully I helped out.